Because the Farouk El-Baz, []vicker, []cal, Da-Teplan, Amber, and the Yuri Gagarin don't have any other references (other than the El-Baz shuttle, which doesn't count), their appearances on the chart aren't problematic. (I'm assuming the Amber isn't the "Aries," and the two ships with partial names also don't equate to other known ship names).

There's also the NCC-30352, whose name is illegible for now, so there's nothing to be done for that yet.

So that leaves 13 ship names that also share names of other ships, most with different registries, most operating at the same time.

Anyway, let's whittle the chart down a tad:

1. U.S.S. Excelsior NCC-21145 - Other than the class ship Excelsior NCC-2000, the only other reference was in TNG "Interface," where a ship of this name was sent to find the U.S.S. Hera. One could plausibly say that it was this ship, not the NCC-2000, that was sent on this mission. It doesn't really contradict anything.
2. U.S.S. Apollo NCC-30000 - While the class ship of the Apollo class should technically be under 1XXXX in registry, there's no reason to assume that this is in fact the class ship. The original class ship could have been decommissioned or destroyed, and this ship could simply be a newer vessel with the same name, and not even of the Apollo class.
3. U.S.S. Hokule'a NCC-30187 - see above.
4. U.S.S. Neil Armstrong NCC-31806 - While technically its name is different from the Challenger class U.S.S. Armstrong, the name is obviously meant to honor the same person. It's also possible that the Neil Armstrong was decommissioned before the other Armstrong was built (anywhere between 2365 and 2373), although I would think that the Armstrong would then have a higher registry than NCC-57537, if registries are chronological.
5. U.S.S. Yorktown NCC-20045 - Because the only other 24th century Yorktown is the Zodiac class NCC-61137, it's entirely possible that this Yorktown was decommissioned before the other one was built, although the latter's registry should probably be a bit higher, but it's still within reason.

6. U.S.S. Lexington NCC-30405- The DS9 episode "Explorers" makes it clear that the Nebula class Lexington NCC-61832 was in operation at least after 2369. So it's possible that this Lexington was decommissioned or destroyed sometime between 2365 and 2369, and the Nebula class ship was its replacement. The newer ship's reg should probably be a bit higher, but it's still within reason.

7. U.S.S. Atlantis NCC-3210 - This is a bit of an anomaly, as both references (this one and the Atlantis NCC-72007) are from displays that were not meant to be taken seriously. So it's debatable whether the ship even exists

So now this leaves six ships that would be classified as problematic:
1. U.S.S. Yamato NCC-24383 - Whatever the accepted registry of the Galaxy class Yamato is, the ship was still in service during "Measure of a Man." That means that either this is at least the third registry for the same ship, or there was another Yamato in service at the same time the Galaxy Yamato was.
2. U.S.S. Constantinople NCC-43622 - This ship was referenced three episodes before "Measure of a Man." The Encyclopedia gives the registry of NCC-34852. While it's possible but unlikely that the ship was destroyed and a newer ship was commissioned within three episodes, the newer ship should probably have a registry of NCC-7XXXX, if registries are chronological. But it's probably supposed to be the same ship.

3. U.S.S. Wellington NCC-33821 - This is obviously supposed to be the same ship referenced in "11001001," but the Encyclopedia gives the registry NCC-28473. Again, that Wellington could have been destroyed or decommissioned the year before and this Wellington could be the replacement, but again the registry should probably be 7XXXX.

4. U.S.S. Saratoga NCC-31640 - Again, this ship could have been destroyed before "Emissary" where we see the NCC-31911 Saratoga, but not only should Sisko's ship's reg be higher if it were brand new, but would Starfleet still be producing Miranda class ships after 2365?

5. U.S.S. Endeavour NCC-25330 - This is the least problematic ship, if we ignore the NCC-39272 from the "Conspiracy" diagram. It's quite possible that this ship was decommissioned and the Nebula class Endeavor NCC-71805 was commissioned around the same time.

6. U.S.S. Excalibur NCC-21534 - Again, this Excalibur could have been destroyed in the few years between "Measure of a Man" and the first time we see the Ambassador class ship in "Redemption," but then why would the newer ship have such a low registry, if regs are chronological?